Method of operating quantum-mechanical memory and computational devices

ABSTRACT

A method of operating a quantum system comprising computational elements, including an insulated ring of superconductive material, and semi-closed rings used as an interface between the computational elements and the external world, is disclosed. In one aspect, the method comprises providing an electrical signal, e.g. a current, in an input ring magnetically coupled to a computational element, which generates a magnetic field in the computational element and sensing the change in the current and/or voltage of an output element magnetically coupled to the computational element. The electrical input signal can be an AC signal or a DC signal. The computational element is electromagnetically coupled with other adjacent computational elements and/or with the interface elements. The corresponding magnetic flux between the computational elements and/or the interface elements acts as an information carrier. Ferromagnetic cores are used to improve the magnetic coupling between adjacent elements.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation-in-part of co-pending U.S. patentapplication Ser. No. 11/364,787, filed Feb. 28, 2006 and entitled“METHOD OF FORMING QUANTUM-MECHANICAL MEMORY AND COMPUTATIONAL DEVICES”,which is a divisional of U.S. Pat. No. 7,042,004, filed Jun. 20, 2003,and entitled “METHOD OF FORMING QUANTUM-MECHANICAL MEMORY ANDCOMPUTATIONAL DEVICES AND DEVICES OBTAINED THEREOF”, which claimspriority to U.S. provisional application No. 60/390,883, filed Jun. 21,2002, and entitled “METHOD FOR FORMING QUANTUM-MECHANICAL MEMORY ANDCOMPUTATIONAL DEVICES AND DEVICES OBTAINED THEREOF.” The entiredisclosure of the foregoing filed applications is hereby incorporated byreference.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to memory and computational devices basedon quantum-mechanical interaction between individual bits. Moreparticularly the present invention relates to solid-state devicescomprising a ring structure as basic element for storing a single bit ofinformation.

2. Description of the Related Technology

During the last decade, quantum computing has become a topic of evergrowing interest, particularly in the field of cryptographyapplications, based on Shor's algorithm for factoring large integers asdisclosed by P. W. Shor in “Algorithms for quantum computing: discretelogarithms and factoring” in Proc. 35^(th) Annual symposium on thefoundations of computer science, 1994, pp 124-123, which is incorporatedherein in its entirety by reference. This is due to the fact that thequantum-mechanical superposition principle allows for a level ofparallel computing that exceeds all classical methods in this field.

A characteristic that differentiates quantum computing from classicalcomputing is the entanglement of the bits. Also in classical computingdevices operating at atomic scale is being developed. Although these“quantum devices” use discrete charge quanta the value of each bit iswell defined: either a “0” or a “1”. In quantum computing however theinterference between subsequent bits may bring the system in entangledmultibit states, which are not accessible in classical computing.

All implementations of such a quantum computer starts with the design ofan individual unit of information processing, the so-called quantum bitor “qbit”.

A first series of approaches addresses the design of this quantum bit atatomic level. The single qbit is realized e.g. as a spinning electron,an atomic nucleus or an oscillating molecule. Whereas these approachesdirectly address the quantum scale, they lack the connection of the qbitto the outside world: input/output structures (I/) ports are not easilyavailable. PCT International Publication No. WO 00/30255, entitled“Crystal Lattice Quantum Computer”, published on May 25, 2002, which isincorporated herein in its entirety by reference, shows a crystallattice computer where the qbit is associated with the orientation ofthe nuclear spin of the atoms.

A second series of similar approaches forms quantum systems but on alarger, nano- or mesoscopic, scale such as quantum dots, nanometer-sizedrings or quantum wires. Although these devices are larger than thedevices of the first approach, they operate similarly as if thesedevices where “artificial or macro-atoms”. Quantum dots are microscopic,carefully tailored regions of a semiconductor surface in which thenumber of electrons is precisely controlled. Axel Lorke et al. disclosesin “Spectroscopy of nanoscopic semiconductor rings”, Phys. Rev Letter84, March 2000, which is incorporated herein in its entirety byreference, the manufacturing of an array of semiconductor quantum ringsstarting from InAs droplets formed on a GaAs surface. The minute ringsallow one or two electrons to circulate in coherent quantum statescorresponding to one of the values of a bit. These quantum states aredependent on the applied large external magnetic field of about 8 Tesla,as is shown by externally providing energy in the form of infraredradiation having the appropriate wavelength to allow transitions betweenthese magnetic-field-dependant quantum states. This external magneticfield is applied uniform over the nanoscopic ring as the rings arepositioned in-between two parallel plates. Although the authorssucceeded in forming qbits on an above-atomic scale, no mention of I/Oports is indicated and the proposed device are for research purposeonly, without giving any information about integration, even of a singleqbit, in a CMOS (complementary Metal Oxide Semiconductor) compatibletechnology.

BRIEF DESCRIPTION OF THE DRAWINGS

All drawings are intended to illustrate some aspects and embodiments ofthe present invention. Devices and fabrication steps are depicted in asimplified way for reason of clarity. Not all alternatives and optionsare shown and therefore the invention is not limited to the content ofthe given drawings.

FIG. 1A illustrates a single closed ring of a quantum system accordingto one embodiment.

FIG. 1B is a ring system with open input and output elements,magnetically coupled using a ferromagnetic core.

FIG. 1C is a matrix of closed rings and open input and output elements.

FIGS. 1D, 1E and 1F illustrate alternative embodiments of thecomputational elements.

FIGS. 2A, 2B, 2C, 2D, and 2E illustrate the switching of the quantumstate of a computational element in accordance with one embodiment.

FIG. 2F shows an example of an input signal.

FIG. 3A shows a sandwich of plates and FIG. 3B shows overlappingelements for improving the magnetic coupling between the elements of thequantum system according to one embodiment.

FIGS. 4A, FIG. 4B, FIG. 4C, FIG. 4D, FIG. 4E, FIG. 4F, and FIG. 4G aremethods for manufacturing a quantum system in accordance with oneembodiment.

FIGS. 5A, FIG. 5B and FIG. 5C are methods for manufacturing a quantumsystem in accordance with an embodiment of the invention.

FIG. 6A, FIG. 6B and FIG. 6C illustrate a method for operating a quantumsystem in accordance with an embodiment of the invention.

FIGS. 7A, 7B, 7C and FIG. 7D show electrical characteristics of aquantum system in accordance with an embodiment of the invention.

SUMMARY OF CERTAIN INVENTIVE ASPECTS

Certain inventive aspects relate to a quantum device for handling and/orstoring bits having a well-defined two-dimensional mathematical basis.

Certain inventive aspects relate to a quantum computational or memorydevice comprising I/O facilities, which do not affect, during or beforeread-out of bits, the quantum states of the individual bits to theextent that information is lost. This device further allows areproducible preparation of the initial state of the qbit afterread-out.

Certain inventive aspects relate to a quantum computational or memorydevice having coherence times that are longer than the computationtimes.

Certain inventive aspects relate to a method for forming quantumcomputational or memory devices in a reproducible and scalable fashionallowing the implementation of these devices on a chip. This methodfurther allows the formation of I/O ports connecting the qbit to theperipheral circuitry of such chip or to the external world. Preferablythe quantum device can be integrated in a semiconductor substrate, usingsemiconductor-processing techniques.

Certain inventive aspects relate to a superconducting quantum ring as acomputational or datastoring element. More specifically this quantum bitor qbit state of such a quantum ring is related to the absence orpresence of persistent currents to be generated by means of a magneticfield.

Coupling between the quantum rings in a matrix and between these quantumrings and these input-output structures is established by inducedmagnetic fields generated by the currents flowing in the quantum ringsand in the input-output structures. The quantum rings are closedstructures in which a closed current flow path is possible. The currentflowing along such closed current flow path will create a magneticfield. The quantum ring is a topological space of genus 1. The quantumring is a closed structure only having one hole. Preferably the quantumrings have a circular cross-section. Preferably the quantum ring hasrounded corners. Preferably the quantum rings have a torus ordoughnut-like shape also known as toroid. The input-output structuresare discontinuous, semi-closed or open rings having two terminals, whichcan be connected to a power source. The current flowing from this powersource along a semi-closed path in the input structure will create amagnetic field as well. The current flowing through one element, e.g.I/O element, qbit, will create a magnetic field, which will induce acurrent in another element, which encloses the field lines of thisinduced magnetic field and as such this subsequent element ismagnetically coupled to the previous element.

In one aspect, a method of forming a device comprising at least twocomputational elements is disclosed. The method comprises depositing ona substrate a superconductive material. The method further comprisespatterning the superconductive material to form the at least twocomputational elements and at least one input-output element. The methodfurther comprises depositing an insulating layer on at least a portionof the patterned computational elements and the patterned input-outputelement.

In another aspect, a method of forming a device comprising at least twoquantum computational elements and one input-output element, eachelement being magnetically coupled to at least one adjacent element bysharing a core, is disclosed. The method comprises depositing a firstlayer made of magnetic material on a substrate. The method furthercomprises patterning the first layer to form at least a lower portion ofa plurality of cores such that each pair of adjacent elements share oneof the cores. The method further comprises depositing a second layermade of dielectric material. The method further comprises depositing athird layer made of superconductive material. The method furthercomprises patterning the third layer to form at least two computationalelements and at least one input-output element, each computationalelement being shaped as a closed loop structure having a single holetherein, each input-output element being shaped as a semi-closed loopstructure, such that the opening of each loop structure overlaps withone of the cores. The method further comprises depositing a fourth layermade of dielectric material. The method further comprises forming one ormore holes in the layers made of dielectric material to expose the lowerportion of the cores, each hole being positioned within the opening ofeach loop structure. The method further comprises depositing a fifthlayer made of magnetic material over the substrate. The method furthercomprises patterning the fifth layer to form an upper portion of thecores.

In yet another aspect, a method of performing a quantum computation isdisclosed. The method comprises applying a magnetic pulse to a quantumcomputational element. The method further comprises causing a change inthe conductive state of the quantum computational element betweensuperconducting and ohmic conduction, the change being responsive toapplying the magnetic pulse.

In another aspect, a method for performing a quantum computation isdisclosed. The quantum device comprises at least one computationalelement. At least one of the computational elements is magneticallycoupled to an input element by sharing the core of a transformer and atleast one of the computational elements is magnetically coupled to anoutput element by sharing the core of a transformer. If more then onecomputational element is present, adjacent computational elements aremagnetically coupled by sharing the core of a transformer. The methodcomprises biasing the output ring, providing an electrical signal to theinput ring, varying the input electrical signal and monitoring thevariation of the output electrical signal with the input electricalsignal. The input electrical signal is preferably a DC signal, such as aDC current. The output electrical signal is preferably a DC signal, suchas a DC current. The method also allows determining the quantum state ofa computational element in a quantum device according to any of theforegoing embodiments. The computational elements are in asuperconducting state, while the output ring switches between asuperconducting state and a non-superconducting state when varying theinput electrical signal.

In another aspect, a method of performing a quantum computation on adevice is disclosed. The device comprises (a) at least two quantumcomputational elements, each computational element being shaped as aring-like structure, wherein each computational element is magneticallycoupled to at least one adjacent computational element by sharing thecore of a transformer, the core comprising a permalloy; and (b) aninterface structure configured to provide magnetic access to at leastone of the computational elements. The method comprises (a) applying amagnetic signal to one of the quantum computational elements of thedevice; and (b) causing a change in the conductive state of thecomputational element between superconducting and ohmic conduction, thechange being responsive to applying the magnetic signal.

In another aspect, a method of performing a quantum operation on adevice is disclosed. The device comprises (a) at least one computationalelement, the computational element being shaped as a ring-likestructure, wherein the computational element is magnetically coupled toat least one adjacent computational element by sharing the core of atransformer, and (b) an interface structure configured to providemagnetic access to the computational element, the interface structurecomprising an input element magnetically coupled to the computationalelement by sharing the core of a transformer and an output elementmagnetically coupled to the computational element by sharing the core ofa transformer. The method comprises providing a direct current (DC) biasto the output element, applying an DC electrical signal to the inputelement, and monitoring the change in the conductive state of the outputelement between superconducting and ohmic conduction when varying theinput electrical signal.

In another aspect, a method of performing a quantum computation isdisclosed. The method comprises applying a magnetic signal to a quantumcomputational element. The method further comprises causing a change inthe conductive state of the computational element betweensuperconducting and ohmic conduction, the change being responsive toapplying the magnetic signal.

DETAILED DESCRIPTION OF CERTAIN ILLUSTRATIVE EMBODIMENTS

In relation to the appended drawings certain embodiments are describedin detail. It is apparent however that a person skilled in the art canimagine several other equivalent embodiments or other ways of executingthe present invention, the spirit and scope of the present inventionbeing limited only by the terms of the appended claims.

In a first aspect the quantization of the information in the quantum bitis disclosed. The quantization of the information in the structure isobtained by using superconducting rings to trap multiples of themagnetic flux quantum in order to maintain persistent currents withinthe qbit. These flux quanta corresponds to clearly distinct and discreteenergy levels.

Deep inside of a superconducting material, no magnetic field will bepresent. If an external magnetic field are to be applied to suchsuperconducting structure this external field would be pushed outwardsof the structure. Such perfect diamagnetism is an inherent property ofsuperconductivity and is called the Meissner-effect. Because of theMeissner-effect the external magnetic field will decay exponentially tozero towards the bulk of superconducting structure. This reduction inmagnetic field requires the presence of a superconducting currentflowing at the outer and/or inner surface of the superconductorstructure, the induced field of which cancels the external field insidethe superconductor. Apart from the transition region near the surfacethe magnetic field and the current density inside the superconductingstructure will therefore be zero. The surface currents of the structurewill adjust themselves if the external magnetic field is changed. Thedepth of the transition region is characterized by the so-calledLondon-penetration depth λL as shown in the following expression forbulk materials at 0 Kelvin, whereby q is twice the electron charge, M iseffective mass of a Cooper pair which is twice the effective mass of anelectron, μ0 is the permeability of the bulk material, ns is the densityof Cooper pairs which is function of temperature T and magnetic field H:

$\begin{matrix}{\lambda_{L} \approx {\frac{1}{q}\sqrt{\frac{M}{\mu_{0}n_{s}}}}} & (1)\end{matrix}$

The London-penetration depth λL is a characteristic of thesuperconducting material: in case of Aluminum λL is about 16 nm at 0Kelvin. In order to have a complete Meissner effect at all surfaces, theouter surface of the superconducting structure must have a minimalspacing in-between so that the transition regions of each surface willnot overlap. Preferably the minimal spacing is much larger than theLondon-penetration depth at a given temperature.

For a ring shaped superconducting structure (1), as shown in FIG. 1A,one can calculate the magnetic flux going through the ring given thefact that the current and the magnetic inside this ring (1) is zero dueto the Meissner effect. Using Ginzburg-London theory it follows that thecurrent density J in the ring is given by

$\begin{matrix}{\overset{->}{J} = {\frac{{- n_{s}}q}{M}\left( {{\hslash {\overset{->}{\nabla}\theta}} + {q\overset{->}{A}}} \right)}} & (2)\end{matrix}$

with n being the electron concentration, q twice the electron charge, Mthe effective mass of a Cooper pair,  reduced Planck's constant, A thevector potential and θ the quantum mechanical phase. Since the currentdensity J has to be zero inside the ring, one concludes:

{right arrow over (∇)}θ=−q{right arrow over (A)}  (3)

Taking the integral along a closed contour “C” inside the ring and usingStokes's theorem to convert a line integral along a contour “C” into asurface integral over the area “O” enclosed by this contour “C”, one canshown that the magnetic flux Φ through this area “O” is equal to

$\begin{matrix}{\Phi = {{s\; \Phi_{0}\mspace{14mu} {where}\mspace{14mu} \Phi_{0}} = \left( \frac{2{\pi\hslash}}{q} \right)}} & (4)\end{matrix}$

with s being an integer.

Formula 4 shows that magnetic flux Φ through the ring can only be aninteger multiple of the elementary flux quantum Φ0, which is equal to2.067810 10-15 Weber.

For a given external field the superconducting current flowing at thesurface of the ring will be such that the total flux through the ringmeets the requirement of equation (4): the sum of the magnetic flux froman external magnetic field and the magnetic flux induced by thesuperconducting current, will always be a multiple of the elementaryflux quantum Φ0.

Certain embodiments use the quantization of magnetic flux through asuperconducting structure (1) to create a qbit. By using superconductivematerials, e.g. preferably Type I superconductors such as Aluminum,Nobium, Lead, Tantalum to create a closed loop structure or torus (1) asshown in FIG. 1A, the resulting superconducting structure (1) can trapmultiples of the so-called elementary or London flux quantum by having acorresponding amount of superconducting current flowing in the ring (1).The logic states of the qbit, e.g. |0>state, |1>states now correspond toa certain magnetic flux quantum which is related to the absence orpresence of a certain amount of current flowing in the ring. Thequantization is not a result from a shrinking of the dimensions of thestructure. Superconducting rings can sustain persistent currents also atlarger dimensions. Typically the rings have a diameter larger than 70 nmeven within the micrometer range, while superconducting rings have beenmanufactured having dimensions in the centimeter range. Hence thisalleviates the need for very small rings and simplifies the productionof qbit structures. Processing techniques already available insemiconductor processes which allow the manufacturing and integrating ofquantum bits in semiconductor chips as will be shown later on. This waythe superconducting rings offer a better approach for integratingquantum bit devices with peripheral circuitry, which can be CMOS-basedcircuitry, while still offering the occurrence of quantum-like behavior.This allows the manufacturing and integrating of quantum bits insemiconductor chips. Although the basic computational element isdescribed as a ring the invention is not limited hereto. More generallyone could describe this element (1) as a torus or as a topological spaceof genus 1; it is closed loop structure having one and only one hole init. The structure itself can have various shapes: circular, elliptical,and polygonal. Preferably the structure has rounded corners. Thediameter of the ring is preferably in the range of 1 to 150 micrometer,while the thickness, i.e. the difference between inner and outerdiameter, of the ring would preferably in the range of 1 to 40micrometer, preferably 1 to 20 micrometer. The minimum height of thering is preferably 0.3 micrometer.

A superconductive material will loose its superconducting property oncethe temperature T exceeds a critical temperature Tc. A temperatureincrease in a superconductor can be caused by external events, e.g.heating, radiation, but also by internal events such as heat dissipationor energy losses within the superconductor due to normal currents, e.g.when switching the quantum states or by eddy currents in the corecoupling two elements (1,2,3). Even if the temperature is below thiscritical temperature superconductivity will break down if the externalmagnetic field H is above a critical magnetic field Hc or, for a givenmaterial, the corresponding magnetic inductance Bc. Aluminum for exampleis a superconductive material having a critical temperature Tc of about1.23 Kelvin and, below this critical temperature, a critical magneticinductance Bc of about 10 milliTesla. Both the critical magnetic fieldHc and the critical temperature Tc are material dependent. Preferablymaterials are used having a transition or critical temperature above 1Kelvin. The superconducting state of a conductor is also characterizedby the “coherence length” which is a measure for the stability of thesuperconducting region or spatial coherence between electrons in asuperconducting phase. The coherence length ξ0 of Aluminum is about 1.6micrometer.

Thus if the magnetic field H in a superconductor exceeds the criticalvalue Hc of this superconductor the conductor will loose itssuperconducting state. A magnetic field can originate from an externalsource or can be induced by the superconducting current itself. If thesuperconducting current density increases due to a time-dependentelectric field circulating in the ring, it will exceed a critical valueJc, corresponding to an induced critical value Hc. Then the ringswitches to the normal state and ohmic dissipation sets in, while themagnetic field inside the ring increases. The superconducting state ofthe ring is lost. This property is used to switch the quantum state ofthe qbit (1). By applying an external magnetic field the superconductorcurrent flowing at the inner and/or outer side of the ring (1) willincrease to compensate this external magnetic field. Finally the currentdensity can be increased above the critical current density Jc. At thismoment the conductor looses its superconducting state and a normal i.e.not-superconducting, current will flow through the ring. This normalcurrent can transfer part of its kinetic energy to the crystal latticeof the conductor resulting in a decrease of the current density belowthe critical value Jc. The component of the total flux through the ring,which is in the direction of the external field, will increase as thecomponent generated by the current through the ring is decreased. Thering can lower its total energy by becoming superconducting again, be itthat the magnetic flux corresponding to the new current density willdiffer from the original flux. The superconducting current required tomaintain the new quantum of magnetic flux is now below the criticalcurrent density by one flux quantum. Applying an input flux thus changesthe quantum state of a qbit, which result in a current exceeding thecritical current density. Preferably only the intended magnetic fieldshould affect the operation of the qbit and the quantum system should beshielded from other, unwanted magnetic fields.

This mechanism is schematically illustrated in FIG. 2A-F, for the caseof two adjacent computational elements (1), however the mechanism isalso applied in the case an input (2) element adjacent to acomputational element (1) or a computational element (1) adjacent to anoutput (3) element. In these FIGS. 2A-e not only these elements will beshown which are relevant to explain the mechanism of changing quantumstate. FIG. 2A shows a vertical cross-section through the two rings (1),while the core (7) is not shown. In this example no current is flowingand no magnetic field is present. The absence of the magnetic field isindicated by stating that the flux through the opening in the rightelement is zero: Φ=0. A time-dependent magnetic field Hext is applied tothe ring on the right, as is indicated in FIG. 2B by the dashed counterline corresponding to the magnetic field lines. This applied field is,in this example, labeled the external magnetic field to distinguish itfrom the magnetic field generated by the superconducting current in theright ring. The latter field will be labeled the induced magnetic fieldHind. The external magnetic field results from a time dependentelectrical field, e.g. a current flowing in the ring on the left: ifthis ring as an input ring (2) then this current is applied from thecircuitry surrounding the quantum system, if this ring is acomputational element (1) this current is the persistent superconductingcurrent flowing in this closed ring (1). In the ring on the left thiscurrent is indicated by a black dot on the right (current flowing intothe page) and a crossed circle on the right (current coming out of thepage), corresponding to the direction in which the current flows. Duethe Meissner effect the total magnetic field Htot inside thesuperconducting right ring must be zero: the external magnetic fieldHext is compensated inside the superconducting right ring by an inducedmagnetic field Hind. Within a distance from the border of the ring,characterized by the London penetration depth λL, the total magneticfield Htot will not be zero but, as explained above decay in anexponential way. The field lines of the induced magnetic field areindicated only on the left part of the ring on the right. This inducedmagnetic field is generated by a superconducting current, which willflow at the inner and outer surfaces of the right ring as indicated bythe black dots at the left and by the crossed circles at the right ofthis ring.

As shown in FIG. 2D the total magnetic field Htot near the borders ofthe right ring will exceed the critical magnetic field Hc and thecurrent density J of the superconducting current in the right ringexceeds a critical current density Jc, whereby the conductor looses itssuperconducting state and a normal i.e. not-superconducting or ohmic,current will flow through the ring. The magnetic field lines willimpinge on the ring and penetrate not only near the border but also overthe whole of the ring. The electrons will not be part of a Cooper pairand they will loose their kinetic energy by dissipation. Consequentlythe current density, which is function of the speed of the electrons,decreases below the critical current density Jc and the right ringbecomes superconducting again. Contrary to the initial state shown inFIG. 2A there are field lines present within the core of the right ringas shown in FIG. 2E. Because the right ring is superconducting again theMeissner effect comes in to play: within the superconducting right ringa persistent current will remain which will cancel the magnetic fieldinside this ring, but this persistent current will be such that the fluxthrough the hole is a integer multiple of the quantum flux, expressed inequation 4.

FIG. 2F gives an example of such an external magnetic field. A pulse isapplied resulting in a magnetic field Hext of a first sign above aminimal level Hmin required to program the quantum bit with one quantumflux. If the quantum ring is to be erased an external magnetic field ofan opposite sign is applied.

In a second aspect of the invention the quantum bit structure and itsinput/output structure are disclosed.

In a first embodiment of the second aspect a quantum bit structure isdisclosed. The design of qbits realized as mesoscopic conducting ringsis disclosed. These objects offer a compromise between the atomic ormolecular level and nanostructure level and allows a quantum behavior,yet large enough to be manufactured using semiconductor processingtechniques in a reproducible way and to allow for I/O ports. Inparticular sets of metal rings are considered, including in- and outputdevices or structures. The quantum-like behavior of the proposed qbit isthe quantization of the magnetic flux trapped by the conducting orsuper-conducting ring as explained above.

FIG. 1B shows a three-ring structure (1,2,3), wherein the ring structure(1) is the basic element of a quantum computer according to oneembodiment. The qbit (1) is located in between two semi-closed rings(2,3). These semi-closed rings can be connected to bonding pads (4)which in turn can be connected to the interconnect circuitry of asemiconductor chip or circuit. This semi-closed or open ring thus servesas an in (2)- or output (3) structure and enables an easy access fromthe external world to the quantum system. Applying an externaltime-dependent current signal Iin to the bonding pads of the inputstructure (2) of the quantum system would produce a changing magneticflux Φin which can induce, in its turn, a current Isuper in the “free”,isolated closed ring (1) adjacent to and magnetically coupled to thisinput port (2). The isolated ring (1) is the computational basic elementof the quantum system. The current Isuper generated in the free ring (1)can also induce by a magnetic flux Φout a current in a neighboring,magnetically coupled, ring and so on. This neighboring ring can be theoutput port (3) of the quantum system and the corresponding current loutgenerated in this output ring (3) can be read out at the bonding padconnected to the output ring (3). The electromagnetic fields generatedby the current flowing trough the semi-closed or closed elements (1,2,3)are used as information carrier in the quantum system. The threeelements could be of equal size, but the input/output rings might havelarger dimensions if needed for connection or heat dissipation purposeswithout effecting the device operation. The open input (2) and/or theoutput (3) ring can be conceived as a solenoid. In this case the outputsignal will be amplified with the number of turns, as is the case in aclassical transformer.

FIG. 1C shows a schematic representation of quantum computer accordingto one embodiment comprising a matrix of n by m (both integers)freestanding, electrically isolated qbits (1), which areelectro-magnetically coupled, with each other (7) and with (5,6) the I/O(input-output) structures (2,3). As can be seen from this Figure the I/Ostructures (2,3) are on the outer edge of the two-dimensional plane ofcomputational elements (1). The I/O structures (2,3) areinterchangeable: the input ring can also be used as an output ringdepending on the direction in which the information flows. The operationof such a quantum computer is depending on the computational algorithmused.

Alternative arrangements are shown in FIG. 1E to 1F. FIG. 1E shows abasic quantum computer comprising two computational elements (1) of asuperconducting material. The two computational elements (1) aremagnetically coupled using a ferromagnetic core (7) whereby eachcomputational element (1) is respectively linked with one of the twolegs of the core (7). The two qbits (1) can be in entangled stateresulting from a quantum-mechanical interaction between the two qbits(1). Both qbits (1) are magnetically accessible: magnetic fields can beinduced and applied to the qbits (1) in order to apply the desired fluxquantum when programming, these flux quantum will result in a certainamount of persistent current in the qbit (1), or magnetic fields can besensed when reading the outcome of the computational operation. Inducingand sensing of magnetic fields can be done using superconducting quantuminterference devices (SQUID) or by using magnetic force microscopy. FIG.1E shows the quantum computer of FIG. 1 in which for inducing or forsensing of the magnetic field a semi-closed structure (2,3) is used.This semi-closed structure (2,3) is magnetically coupled to an adjacentcomputational element (1) using a ferromagnetic core (5,6). A currentflowing through this semi-closed structure (2,3) will induce a magneticfield, which will result in a persistent current in the computationalelement (1). In its turn such a persistent current, more precisely theflux quantum generating this current can induce a current in a adjacentsemi-closed structure (2,3) which is magnetically coupled to thiscomputational element (1). FIG. 1F shows the quantum computer of FIG. 1Ewherein for inducing (2) as well as for sensing (3) the magnetic fieldssemi-closed structures (2,3) are used. One semi-closed structure (2) isused as input element to induce a magnetic flux quantum, which ismagnetically coupled (5) to an adjacent computational element (1). Thiscomputational element (1) is magnetically coupled (7) to anotheradjacent computational element (1), which in its turn is magneticallycoupled (6) to another semi-closed structure (3). This semi-closesstructure (3) is used as an output element to sense the induced magneticfield.

In a second embodiment of the second aspect methods and means forimproving the magnetic coupling between the elements of the quantum bitdevice are disclosed. The quantization of the information carried by themagnetic flux as well as the guidance of the magnetic flux betweenadjacent rings as well as is a feature of one embodiment. A largeramount of the magnetic field lines is found to spread out in space andtherefore appropriate flux guiding has to be achieved to minimize orcancel information loss, thereby setting the classical basis for thedisclosed device. The better the magnetic coupling between the qbits (1)amongst themselves and between the qbits and the I/O structures (2,3),the better the coherence between the individual bits.

FIG. 3A illustrates an embodiment in which the magnetic coupling betweenthe elements of the quantum system is improved by sandwiching thequantum system between two plates (7) of superconducting material. Dueto the Meissner effect the magnetic field is confined within the top andbottom plates (7). The dotted lines denotes the magnetic field squeezeddue the Meissner effect of superconducting top and bottom plate (7).This way more magnetic field lines will pass through the core ofadjacent rings.

FIG. 3B illustrates an embodiment in which the magnetic coupling isimproved by positioning the elements (1,2,3) of the quantum systemalternating in different planes and having the rings (1,2,3) partiallyoverlapping each other. In this embodiment the structures (1,2,3) arealternately formed on different planes. Within each plane the structureis positioned so as to at least overlap partially with the structuresformed on a plane above or below the plane at which the currentstructure is positioned. The floating ring (1) shares two cores with theinput (2) and output (3) ring. The in- and output rings are situated ina ground plane, whereas the free ring is put in an adjacent level withpreferably half of its area above the input port and half of it coveringthe output port.

FIG. 1B illustrates a preferred embodiment in which the magneticcoupling is improved by including a ferromagnetic core (5,6,7) betweenthe elements (1,2,3) to create a transformer-like structure.Ferromagnetic cores between the rings are used similar to the case of atransformer in macro-scale transformers. These cores should be fullyclosed and pass through the holes of the elements (1,2,3) withouttouching them. Preferably a soft permalloy with a high permeability isused, such as Nickel-Iron. As shown in FIG. 1B, the input ring (2) andthe qbit (1) are connected by a metal core (5) thereby forming atransformer. The magnetic field lines giving rise to a flux Φin areconcentrated within this core and the field losses are reduced. As shownin FIG. 1C for a quantum system each element in the array of the qbitcells is connected with its neighboring qbits by a metal core (7) orwith an input/output element (2,3) by a metal core (5,6). In thisexample each qbit (1) shares 4 cores (5,6,7) with its adjacent qbits (1)or with an I/O element (2,3). The cross-sectional area of the coreshould preferably be as large as possible and constant along the core asthis will determine the maximum magnetic inductance B in the core. Thevertical part (5 b, 6 b) of the core should cover as much as possiblethe area of the ring opening without touching the ring itself. The top(5 c, 6 c) and bottom parts (5 a, 6 a) of the core should preferably beas thick as possible.

Note that the input/output elements (2,3) are not coupled with adjacentinput/output elements (2,3). These elements (2,3) are in directelectrical contact with the outside world and consequently theseelements are generally not in a superconducting state. These elements(2,3) should have a good normal conductivity.

In a third aspect of the invention alternative process sequences aregiven to manufacture the quantum bit in a fashion, compatible withsemiconductor or CMOS Processing. One of the advantages for theexemplary embodiment is that process steps and methods known insemiconductor processing can be used to manufacture the devices. Metallayers can be deposited using e.g. Chemical-Vapor-Deposition (CVD),Physical-Vapor-Deposition (PVD), sputtering techniques, spin-on orelectrochemical plating techniques. Dielectric layers can be formed e.g.by CVD, by spin-on depositing techniques. Dielectric layers can beplanarized by using chemical-mechanical-polishing (CMP, by etch-back oflayers, by coating layers with spin-on-materials. Layers are patternedusing lithographic processes in which a pattern is transferred by usinge.g. optical, Ultra-Violet or E-beam lithography to a photosensitivelayer formed on this layer. This patterned photosensitive layer can thenbe used to transfer the pattern to the underlying layer(s) andafterwards the photosensitive layer is removed leaving only thepatterned layer. This transfer can be done by using wet etching, dryetching or by lift-off techniques. Where appropriate cleaning steps willbe performed to deposition steps or after removal steps. Persons skilledin semiconductor process technology know all such steps.

In the light of the above, a person skilled in the art would realizethat for ease of processing using state-of-the-art technology all layeror structure heights should preferably be in the range of 50 to 300nanometer, but less than 5 micrometer.

In a first embodiment of the third aspect a process sequence isdisclosed which doesn't require the use of electrochemical depositionprocesses. The process sequence is illustrated in FIGS. 4A-g, whichcorresponds to the basic set of 3 elements (1,2,3) shown in FIG. 1B. Aperson skilled in the art will appreciate that this process sequence canalso be used to form a quantum system illustrated in FIG. 1C. Forexample the parts of core (6) between isolated rings (1) is formedtogether with their counterparts of the cores (5,6,) connecting theqbits (1) with the I/O rings (2,3).

First a substrate (10) is provided as shown in FIG. 4A. This substratecan be a semiconductor substrate as used in CMOS processing: silicon,silicon-on-insulator, germanium, gallium-arsenide. The substrate canalso be a ceramic or thin-film substrate. The substrate can be a blanketsubstrate, optionally covered with a dielectric layer, e.g. an oxide.Electronic circuitry might already be present on this substrate, e.g.transistors might already be formed, interconnect levels might bepresent. Such underlying electronic circuitry is covered with aninsulating layer separating the quantum structures from underlyingdevices or conductors.

On top of this substrate (10) the bottom part (5 a, 6 a) of the cores(5,6) is formed. A layer of a first metal (11) is deposited andpatterned to form the bottom part of the cores as shown in FIG. 4B. Thisfirst metal is made of a magnetic material, preferably a soft permalloysuch as NiFe or an alloy thereof. This material, which will be part ofthe core, should have a high saturation magnetic field and a lowhysterisis.

As shown in FIG. 4C the bottom part (5 a, 6 a) of the cores (5,6) iscovered with a first dielectric layer (12), which will form part of theinsulation between the cores (5,6) and the rings (1,2,3) of the quantumsystem. The outer surface of this first dielectric layer (11) shouldpreferably be planar in order to control topographical effects on therings (1,2,3), which will be formed on this surface. Optionally aplanarization step such as CMP can be applied, in which an initialthicker layer is polished down to the desired layer thickness andplanarity. This first dielectric layer can be an oxide or nitride layer.

On top of this first dielectric layer (12) the bonding pads (4, notshown), input (2)/outputs (3) elements, the qbits (1) are formed. Asecond metal layer (13) is deposited on the first dielectric layer (12)and patterned to form respectively the bonding pads (not shown)connected to the input ring (2), the input ring (2), the isolated ring(1), the output ring (3) and the bonding pads (4) connected to theoutput ring (3). This second metal layer is a layer of a superconductivematerial such as a metal (Aluminum, Niobium). The ring structures(1,2,3) are patterned such that the bottom part (5 a, 6 a) of the coresoverlaps with the opening of the corresponding rings. The opening of theinput (2)/output (3) rings is aligned with the outer end of respectivelythe bottom parts (5 a, 6 a), while the opening of the qbit (1) isaligned with the inner ends of both bottom parts (5 a, 6 a) as shown inFIG. 4D.

As shown in FIG. 4E the substrate is again covered with a dielectriclayer (14), which will form part of the insulation between the cores(5,6) and the rings (1,2,3) of the quantum system. The outer surface ofthis second dielectric layer (14) should preferably be planar in orderto control topographical effects rings (1,2,3), which will be formed onthis surface. Optionally a planarization step such as CMP can beapplied, in which an initial thicker layer is polished down to thedesired layer thickness and planarity. This second dielectric layer canbe e.g. an oxide or nitride layer.

As shown in FIG. 4 f openings (15) are formed throughout the first (12)and second (14) dielectric layers to expose the first metal layer (11).These openings (15) are aligned with the openings of the rings (1,2,3)and with the ends of the bottom parts (5 a, 6 a). The openings (15) canbe etched stopping on the first metal layer (11) or on the substrate(10) underneath this first metal layer (11). Optionally a dedicatedlayer (not shown) can be provided on top of the first metal layer (11)or on top of the substrate (10) to be used as an etch stop layer.Preferably this etch stop layer also is selected from the group ofmagnetic materials. If a non-magnetic material is used as etch-stoplayer, this layer should be removed as to expose the first metal layer(11) at the bottom of the openings (15). These openings will later on bemetalized to constitute the uprising or vertical parts (5 b, 6 b) of thecores (5,6) connecting the bottom (5 a, 6 a) and top (5 b, 6 b) parts ofthe cores (5,6).

After forming the openings (15) a second metal layer (16) is depositedover the substrate. This second metal layer is patterned to form the topparts (5 c, 6 c) of the cores (5,6), which overlap the openings (15)whereby the second metal layer (15) covers at least the sidewalls andthe bottom of the openings (15) in order to form the vertical parts (5b, 6 b) of the cores (5,6) contacting the bottom and the top parts ofthe cores as shown in FIG. 4 g.

Additionally a passivation layer (not shown) can be deposited over thesubstrate to protect the quantum system. This passivation layer can bee.g. a bilayer of oxide and nitride or a monolayer thereof. Openings areetched in this passivation layer to expose the bonding pads (4, notshown) in order to allow contacting of the quantum system.

In a second embodiment of the third aspect a process sequence isdisclosed which uses electrochemical deposition processes, in thisexample electroplating. The process sequence is illustrated in FIGS.4A-c, which corresponds to the basic set of 3 elements (1,2,3) shown inFIG. 1B.

After providing a substrate (10) a conductive layer (18) is deposited asshown in FIG. 5A. This conductive layer (18) will be used during theelectroplating process. Preferably this conductive layer (18) is anon-magnetic metal such as Copper or Gold as to prevent leakage ofmagnetic field lines from the cores (5,6,7) and unwanted coupling ofqbits via this common conductive layer (18).

The processing steps of the embodiment illustrated in FIG. 4A-g areused: formation of the bottom parts of the cores, deposition of a firstdielectric layer (12), formation of the bonding pads (4) and rings(1,2,3), deposition of a second dielectric layer (14), opening of thecontact holes (15), deposition and patterning of a second metal layer(16) to form the top parts (5 c, 6 c) of the cores (5,6) overlapping theopenings (15) whereby the second metal layer (15) covers at least thesidewalls and the bottom of the openings (15). (see FIG. 5A).

In order to increase the thickness of the core (5,6) an electroplatingprocess is used. During this process the conductive layer (18) is biasedand additional magnetic material is deposited on the patterned secondmetal layer (15) to increase the thickness of the vertical (5 b, 6 b)and top parts (5 c, 6 c) of the cores (5,6). (see FIG. 5C). Optionallyalso the thickness of the bottom parts (5 a, 6 a) can be increased by anapplying an electroplating process to add additional magnetic materialto these bottom parts prior to the deposition of the first dielectriclayer (12). In yet another option electroplating is used to fill theopenings (15) with magnetic material and afterwards the second metallayer (16) is deposited over the substrate. This second metal layer ispatterned to form the top parts (5 c, 6 c) of the cores (5,6), whichoverlap the already filled openings (15).

Additionally a passivation layer (not shown) can be deposited over thesubstrate to protect the quantum system. This passivation layer can bee.g. a bilayer of oxide and nitride or a monolayer thereof. Openings areetched in this passivation layer to expose the bonding pads (4) in orderto allow contacting of the quantum system.

One exemplary embodiment is disclosed below.

Structures are designed, consisting of basic aluminum ring arrangements(in-(2) and out (3) put rings and computing element (1)) as well as theferromagnetic cores (5,6,7), made of nickel-iron (NiFe). Aluminum is atype I superconductor and the samples that are used in-house are foundto be superconducting for temperatures below 1.23 K. NiFe has a relativepermeability of about 75000. The structures are designed for evaluationpurposes in such a way that it is possible to perform electricalmeasurements as well as low temperature measurements using magneticforce microscopy (MFM). These experiments enabled us to verify atransformer-type effect of magnetic coupling and also if the fluxquantization effect is compatible with the presence of persistentcurrents in the ring. The layout is realized, using lithography masksand standard processing techniques, such as deposition, etching andlift-off. In total, four device layers are present, embedded on asubstrate, using three masks:

-   -   Mask for bottom core-parts (5 a, 6 a), which is re-used to form        the top coreparts (5 c, 6 c)    -   Mask for rings (1,2,3) and bonding pads    -   Mask for core-tips (5 b, 6 b),

The structures are drawn using the Cadence Virtuoso software. Theyinclude 15 micrometer diameter rings with thicknesses of 2 micrometer.The cores and tips are designed in such a way that all gaps, separationsand minimal distances are 2 micrometer. Optical alignment structures anda passivation layer are included as well. The corresponding opticallithography masks are made in-house. A process-flow is set up, usingthese masks to build the device on two-inch Si wafers in about twentyprocessing steps. The crucial step is to connect the top and bottomparts of the cores by making trenches (15) going through the rings, butnot touching them. These trenches (15) are needed for the core-tips asto form closed structures. Simulations have supported the idea of usingthe ferromagnetic cores. 99% of the flux can be guided from an inputring (2) to a free ring (1), and 49% of that flux can be guided to anoutput ring (3). Two cores (5,6) share the available area on the freering (1). There is sufficient coupling to get enough flux for creating apersistent current in a superconducting ring (1). The small cores enableus to use low current signals and still achieve relatively high magneticfields which doesn't exceed the critical field strength of thesuperconductive material used. In one example a system comprising threerings of 6 micrometer diameter and thickness of 1 micrometer aresimulated, using NiFe cores of permeability 75000. An input current of10 mA in the first ring produced fields up to 0.118 T inside the coresand is sufficient to achieve the desired coupling. A soft permalloy withhigh permeability will switch its magnetic moments, according to thefrequency of the driving signal, and continuously guide the flux fromone ring to another. Signals in the range of a few micro-Ampere up to100 milli-Ampere with frequencies below 100 MHz are sufficient to notexceed the saturation field of the permalloy and also to enablesynchronized switching between the core and the magnetic field. Theresults indicate that using superconducting aluminum rings incombination with the ferromagnetic cores (permalloy NiFe, <75000) aresuitable candidates as quantum bits. Injecting input currents of 1 mA,alike the signal shown in FIG. 2F, up to frequencies of 1-10 MHzproduces magnetic fields of around 1 T inside the cores, just below thesaturation point of the permalloy (1.1 T). The flux coupling achieveddepends on the spatial arrangement of the cores. In order to trap one ormultiples of the London flux quantum φ₀, a minimum coupling of 50% isrequired between the input ring and the floating ring (computingelement). The local fluxes are in the order of 10⁻¹³ Wb and animprovement to the free-field case of about two to three times 10² isachieved. The simulations confirmed the feasibility of the qbitarchitecture and the structures are currently being processed, becausethe devices under investigation are not only capable of emulating aregister of quantum bits but also contain extremely small transformerswith permalloy cores to improve the flux guiding.

As outlined in FIGS. 2 a-2F and the corresponding description above, thequantum computational device behaves like a transformer over a broadrange of temperatures and applied signals when a time-dependent magneticfield H is applied, resulting from a time dependent electrical field,e.g. by a current, in particular an alternating current (AC), flowing inone of the I/O elements (2, 3). However the output electrical signal isdependent not only on the input electrical signal and the quantum stateof the inner ring(s) (1) but also on other effects which would result ina variation of the magnetic field through the output element (3), e.g.variation in material parameters, external magnetic fields, . . . .

When a direct current (DC) is applied to either one of the I/O ports (2,3) a signal transfer from the input element (2) through the device tothe output element (3) is only possible when the computational elements(1) are in the superconducting state. The electrical signal in theoutput element (3) depends on the electrical signal in the input ring(1) and on the quantum state(s) of the computational element(s) (1)which are coupled to this input element (2) and this output element (3)and to each-other. These computational element(s) (1) are in asuperconducting state such that the current therein is subject to fluxquantization.

The operation of the device in case a DC current is applied isillustrated in FIGS. 6A and 6B. An electrical signal, such as a DCcurrent I_(in), provided to the input ring (2) induces a static magneticfield H_(ext) which is transferred to the isolated superconducting ring(1) through the first permalloy core (5) shared between the inputelement (2) and the inner ring (1). Since the total magnetic fieldH_(tot) through a closed superconducting ring (1) is governed by fluxquantization, a screening current I_(super) is induced in this isolatedring (1) thereby creating a magnetic field H_(ind) in the central partof the isolated ring (1). Part of this magnetic field, subject to theflux quantization condition, will be captured by the second permalloycore (6) and being transferred to the output ring (3) shared between theinner ring (1) and the output ring (3). Changes in the magnetic fieldH_(ind) (or magnetic flux F_(ind)) captured by the output ring (3) canbe detected via a corresponding change in the critical current I_(c) ofthe output ring. The output ring (3) is thus also biased to have currentflowing therein. By measuring the current-voltage characteristic of theoutput ring (3) and correlating this characteristic with the magneticflux from the central ring (1), allows providing information about thequantum state of the central ring (1).

When the input current I_(in) and, consequently, the total magneticfield H_(tot) through the isolated ring (1) becomes large enough, thestate of this isolated ring (1) changes as illustrated in FIG. 6B. Morespecifically, when the total field H_(tot) in the central ring (1)becomes nΦ₀+Φ₀/2, with n being an integer, Φ₀=h/2e being the fluxquantum, the number of flux quanta enclosed by this ring (1) increasesby one thereby changing to (n+1)Φ₀. When this flux state switch occurs,the screening current in the isolated ring (1) is maximal. With furtherincrease of the input magnetic field H_(ext) the screening currentI_(super) in the ring (1) decreases and will vanish when the externalfield H_(ext) equals the number of flux quanta trapped in the isolatedring (1), as already discussed above with regard to FIGS. 2 a-2F.

The described changes in the flux state of the isolated ring (1) aredetected by measuring the current-voltage characteristic of the outputring (3) (V_(out) vs I_(out)) and monitoring the change in the criticalcurrent I_(c) of the output current. The critical output current I_(c)depends on the screening magnetic field H_(ind) which is transferredfrom the central ring (1) through the second permalloy core (6) to theoutput element (3). When sweeping the input electrical signal, e.g.current I_(in) or voltage at the input element (1), a maximal screeningcurrent I_(super) and corresponding screening field H_(ind) resultscorresponding to the lowest critical current of the output ring, whereasthe absence of the a screening current I_(super) in the ring (1) isdetected by a higher critical current at the output ring (3). Theinitial critical current of the superconducting output element (3) canbe determined by measuring the current-voltage characteristic of theoutput ring (3) (V_(out) vs I_(out)) and determining from thischaracteristic for which value of the output electrical signal theconducting state of the output ring (3) changes between thesuperconducting state, i.e. where the output voltage remains essentiallyconstant with varying output current, and ohmic state i.e. where theoutput voltage varies with output current.

A schematic overview of the experimental procedure is provided in FIG.6C, showing the magnetic flux for the different circuit elements asfunction of the input current I_(in). Inside the experimental window(indicated by the dashed box), the input current I_(in) is plotted overa symmetric sweep range spanning a region where the screening currentI_(super) maintains a zero magnetic flux ground state (labeled I) and aregion where one flux quantum is trapped in the central ring (1)denoting the next higher quantum state ±h/2e (labeled region II). On thevertical axis one observes a steady increase in the input flux Φ_(in)(H_(ext)) with increasing input current I_(in) and consequently a linearincrease of the flux Φ_(A) inside the first permalloy core (5) which iscoupled to the closed ring (1). A screening field H_(ind) at the closedring (1) assures that the total flux Φ_(tpt) (field H_(tot)) of thisring stays constant with respect to Φ_(A), changing by an amount of h/2eonly when the incoming flux signal Φ_(in) (field H_(ext)) satisfies thequantization condition, i.e. when going from region I to region II. Theflux Φ_(B) (field H_(ind)) transferred from the closed ring (1) to theoutput ring (3) via the second core (6) carries both the screening andthe quantization signatures of the closed ring (1) to the output ring(3).

The operation principle outlined in the previous paragraphs is validatedby manufacturing the device shown in FIG. 1B on a standard silicon wafer(10) using known lithography and sputtering and chemical vapordeposition (CVD) deposition techniques, as for example illustrated byFIGS. 4A-G and the corresponding description. In this example, the threerings (1, 2, 3) are made of about 30 nm thick Al films with a diameterof about 26.8 μm and a ring width of about 2.9 μm. The spacing betweenadjacent rings (1-2, 2-3) is about 1.3 μm. The permalloy cores (5, 6)are made of a NiFe alloy. They are about 20 μm wide, 31 μm long andabout 270 nm thick (5 b, 6 b) in the centre of the Al rings (1, 2, 3).The planar parts (5 a, 5 c, 5 c, 6 c) of the cores (5, 6) above andbelow the level of these Al rings (1, 2, 3) are about 50 nm thick. Thespacing between the two cores in middle ring (1) is about 1 μm. Thedifferent metals use to form the rings (1, 2,3) and the cores (5, 6) areisolated from each-other by silicon-nitride layers (12, 14). The deviceis passivated and contact holes ware dry etching through thispassivation layer to contact the input ring (2) and the output ring (3).The superconducting transition temperature of the thin Al film of therings (1, 2, 3) is found to be about Tc˜1.45 K.

FIGS. 7A and B show the experimental demonstration of controlledDC-current induced flux quantization in the isolated superconductingring (1). FIG. 7A shows a surface plot displaying the evolution of thesuperconducting-to-normal conducting state transition in the V_(out)I_(out) characteristic when the input current I_(in) is varied atemperature T=1.22K. The current I_(out) of the output ring (3) is sweptclose to its critical value I_(c) for each I_(in) step at the input ring(2). When the input current I_(in) is 0 uA, the output ring exhibits atransition from the superconducting to the normal conducting regime atI_(c)˜22 uA. Raising the input current I_(in) induces a continuousdecrease of this critical current I_(c) due to the increasing magneticflux Φ_(B) (H_(ind)) transferred through the superconductingDC-transformer (6) because of the screening effect (H_(ind)) in theisolated ring (1). The decrease of the critical current I_(c) of theoutput current I_(out) for the superconducting-to-normal transition isindicated with the dashed line in FIG. 7A left. At an input currentI_(in) of about 250 uA, i.e. well above the superconducting-to-normalstate transition in the input ring (1), the critical current I_(c) inthe output ring (3) abruptly jumps from about 19.5 uA to 21 uA. This isshown in the inset of FIG. 7A by the dashed line, giving a top-down viewalong the V_(out) axis onto the I_(in)-I_(out) plane. At the position ofthe arrow the critical current value I_(c) abruptly increases. Asexplained above, such a change in the critical current I_(c) of theoutput ring (3) towards higher values is consistent with the capture ofa flux quantum inside the isolated ring (1). Once a quantum flux istrapped, the central ring (1) further screens the input magnetic fluxΦ_(A) (H_(ext)) so that the output critical current decreases againabove I_(in)=250 uA. Notice that the read-out current I_(out) is morethan 1 order of magnitude lower than the input current I_(in) at thetransition, implying that the influence of the output ring (3) on thequantum state of the isolated ring (1) is much weaker than the influenceof the input ring (2) thereon.

For read-out purposes, the output ring is also fixed-biased close thesuperconducting-to-normal transition at similar temperature as the innerring (1). FIG. 7B shows the output voltage V_(out) as a function of theinput current. In this example the output current I_(out) is 19 uA forthe input current I_(in) a range from about −350 uA to 350 uA at atemperature of about 1.28K. The output voltage V_(out) is here used as ameasure for the magnetic field at the output. The variation of theoutput voltage with input current is remarkably symmetric with respectto I_(in)=0 A. The output voltage V_(out) increases with absolute valueof the input current |I_(in)| before exhibiting a step-like decrease atan absolute value of the input current |I_(in)| of about 200-250 uA.These steps are physically reversible—they occur in the same range ofinput current, independent of the current sweep direction—so that theisolated ring (1) can be controllably switched between a ground stateand a higher state, i.e. a quantum flux trapped in the quantum ring (2).The flux quanta trapped at the equal, but opposite, input currentscorrespond to opposite magnetic flux directions in both the isolated (1)and the output ring (3).

When the isolated middle ring (1) is in the normal state, e.g. at atemperature above the transition temperature of the superconductinginner ring (1), the persistent current I_(super) in the middle ring (1)vanishes thereby breaking the magnetic flux transfer between the rings(2,3). The DC superconducting transformer (6) is disabled. As a result,the dependence of the output ring voltage V_(out) on the input ringI_(in) current disappears. This is illustrated FIG. 7C showing a flatV_(out) vs. I_(in) characteristic at T=4.2 K compared to the FIG. 7Dshowing a V_(out) vs. I_(in) characteristic having a step-like behaviorin the superconducting state under the same bias conditions.

The foregoing description details certain embodiments of the invention.It will be appreciated, however, that no matter how detailed theforegoing appears in text, the invention may be practiced in many ways.It should be noted that the use of particular terminology whendescribing certain features or aspects of the invention should not betaken to imply that the terminology is being re-defined herein to berestricted to including any specific characteristics of the features oraspects of the invention with which that terminology is associated.

While the above detailed description has shown, described, and pointedout novel features of the invention as applied to various embodiments,it will be understood that various omissions, substitutions, and changesin the form and details of the device or process illustrated may be madeby those skilled in the technology without departing from the spirit ofthe invention. The scope of the invention is indicated by the appendedclaims rather than by the foregoing description. All changes which comewithin the meaning and range of equivalency of the claims are to beembraced within their scope.

1. A method of performing a quantum computation on a device, the devicecomprising: at least two quantum computational elements, eachcomputational element being shaped as a ring-like structure, whereineach computational element is magnetically coupled to at least oneadjacent computational element by sharing the core of a transformer, thecore comprising a permalloy; and an interface structure configured toprovide magnetic access to at least one of the computational elements,the method comprising: applying a magnetic signal to one of the quantumcomputational elements of the device; and causing a change in theconductive state of the computational element between superconductingand ohmic conduction, the change being responsive to applying themagnetic signal.
 2. The method of claim 1, wherein the magnetic signalis applied from an external source to the quantum computational element.3. The method of claim 2, wherein the interface structure comprises aninput element magnetically coupled to the computational element, and themagnetic signal is applied to the quantum computational element byapplying an electrical signal to the input element.
 4. The method ofclaim 3, wherein the input element is magnetically coupled to thecomputational element by sharing the core of a transformer, the corecomprising a permalloy.
 5. The method of claim 3, further comprisingsensing a magnetic field generated by the quantum computational elementto read the outcome of the quantum computation.
 6. The method of claim5, wherein the interface structure comprises an output elementmagnetically coupled to the computational element and the magnetic fieldis sensed by the output element, the magnetic field creating anelectrical signal in the output element.
 7. The method of claim 3,wherein the input electrical signal is a direct current (DC) signal. 8.The method of claim 7, further comprising sensing a magnetic fieldgenerated by the quantum computational element to read the outcome ofthe quantum computation.
 9. The method of claim 8, wherein the interfacestructure comprises an output element magnetically coupled to thecomputational element and the magnetic field is sensed by the outputelement.
 10. The method of claim 9, wherein the sensing of the magneticfield by the output element comprises causing a change in the conductivestate of the output element between superconducting and ohmicconduction.
 11. A method of performing a quantum operation on a device,the device comprising: at least one computational element, thecomputational element being shaped as a ring-like structure, wherein thecomputational element is magnetically coupled to at least one adjacentcomputational element by sharing the core of a transformer, and aninterface structure configured to provide magnetic access to thecomputational element, the interface structure comprising an inputelement magnetically coupled to the computational element by sharing thecore of a transformer and an output element magnetically coupled to thecomputational element by sharing the core of a transformer, the methodcomprising: providing a direct current (DC) bias to the output element;applying an DC electrical signal to the input element; and monitoringthe change in the conductive state of the output element betweensuperconducting and ohmic conduction when varying the input electricalsignal.
 12. The method of claim 11, wherein monitoring the change inconductive state comprises monitoring the output electrical voltagewhile varying the input electrical signal.
 13. The method of claim 11,wherein the core of each transformer comprises a permalloy.
 14. A methodof performing a quantum computation, the method comprising: applying amagnetic signal to a quantum computational element; and causing a changein the conductive state of the computational element betweensuperconducting and ohmic conduction, the change being responsive toapplying the magnetic signal.